Several challenges have to be overcome. The first challenge comes from physics itself. Unusual or unexpected signatures of long-lived particles may arise. For example, decays could occur outside the usual, dedicated detectors. Monte-Carlo generators need to be developed in accord with theoretical progress, and therefore samples with simulated data may not be readily available.
In order to be as model-independent as possible, searches are usually signature-driven. One looks for displaced or delayed decays, or even particles trapped in detector material. The MoEDAL experiment [1]} at CERN, for example, will search for magnetic monopoles in sections of an old CMS beam pipe.
Displaced decays with respect to the primary interaction vertex can manifest themselves in a number of ways, for instance as displaced multi-track vertices, photons, dileptons or lepton-jets. Displaced jets may have particular properties. Jets with multi-track vertices may appear not only in the inner tracking system, but also in the muon chambers. The characteristic signature of emerging jets [2]} are displaced tracks and many different vertices inside the jet cone. Trackless jets, on the other hand, have a low fraction of electromagnetic energy besides no tracks in the inner tracking detector. Figure REF  shows a sketch of the different displaced decays in a collider detector. Another signature for LLP's are delayed decays, which require out-of-time detection.
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